How to plot the "feasible region" in Maple16 given two inequalities?

Question

We are given two inequalities:

$g_1: x^2 + y^2 - z - 1 \leq 0$

$g_2: x^2 + y^2 + z -2 \leq 0$

Plot the feasible region.

Well, I know the boundaries of the feasible region because;

If:

$x,y = 0$ then $z \geq -1$ and $z \geq 2$

$x,z = 0$ then $-1 \leq y \leq 1$ and $-\sqrt 2 \leq y \leq \sqrt 2$

$y,z = 0$ then $-1 \leq x \leq 1$ and $-\sqrt 2 \leq x \leq \sqrt 2$

Is it true that if $x = \sqrt 2$ it will not satisfy $g_1$.

So the boundaries of the feasible region is

$-1 \leq z \leq 2, -1 \leq y,x \leq 1$.

Then I can draw it and I get "a lemon" form 3d graph, but it is not as nice as if I would get Maple to plot it for me, but how?

Answer 1

Maple does not have a 3-D visualization of the feasible region of a set of inequalities; the 2-D version is implemented as plots:-inequal. Nevertheless for this particular example, you can get what you want by creating a stack of 2-D visualizations using plots:-inequal:

> f := z -> plots:-inequal( {x^2+y^2-z-1<=0, x^2+y^2+z-2<=0}, x=-2..2, y=-2..2 );
> plots:-display( seq( plottools:-transform((x,y)->[x,y,z])(f(z)), z=-1.2..2.2, 0.2 ) );